Vol. 12, No. 5, 2018

Download this article
Download this article For screen
For printing
Recent Issues

Volume 18
Issue 7, 1221–1401
Issue 6, 1039–1219
Issue 5, 847–1038
Issue 4, 631–846
Issue 3, 409–629
Issue 2, 209–408
Issue 1, 1–208

Volume 17, 12 issues

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
Editors' interests
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author index
To appear
Other MSP journals
Polynomial bound for the nilpotency index of finitely generated nil algebras

Mátyás Domokos

Vol. 12 (2018), No. 5, 1233–1242

Working over an infinite field of positive characteristic, an upper bound is given for the nilpotency index of a finitely generated nil algebra of bounded nil index n in terms of the maximal degree in a minimal homogenous generating system of the ring of simultaneous conjugation invariants of tuples of n-by-n matrices. This is deduced from a result of Zubkov. As a consequence, a recent degree bound due to Derksen and Makam for the generators of the ring of matrix invariants yields an upper bound for the nilpotency index of a finitely generated nil algebra that is polynomial in the number of generators and the nil index. Furthermore, a characteristic free treatment is given to Kuzmin’s lower bound for the nilpotency index.

nil algebra, nilpotent algebra, matrix invariant, degree bound
Mathematical Subject Classification 2010
Primary: 16R10
Secondary: 13A50, 15A72, 16R30
Received: 27 June 2017
Accepted: 29 March 2018
Published: 31 July 2018
Mátyás Domokos
MTA Alfréd Rényi Institute of Mathematics
Hungarian Academy of Sciences